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<pre>
      SUBROUTINE <a name="SLASY2.1"></a><a href="slasy2.f.html#SLASY2.1">SLASY2</a>( LTRANL, LTRANR, ISGN, N1, N2, TL, LDTL, TR,
     $                   LDTR, B, LDB, SCALE, X, LDX, XNORM, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      LOGICAL            LTRANL, LTRANR
      INTEGER            INFO, ISGN, LDB, LDTL, LDTR, LDX, N1, N2
      REAL               SCALE, XNORM
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      REAL               B( LDB, * ), TL( LDTL, * ), TR( LDTR, * ),
     $                   X( LDX, * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="SLASY2.21"></a><a href="slasy2.f.html#SLASY2.1">SLASY2</a> solves for the N1 by N2 matrix X, 1 &lt;= N1,N2 &lt;= 2, in
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">         op(TL)*X + ISGN*X*op(TR) = SCALE*B,
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  where TL is N1 by N1, TR is N2 by N2, B is N1 by N2, and ISGN = 1 or
</span><span class="comment">*</span><span class="comment">  -1.  op(T) = T or T', where T' denotes the transpose of T.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LTRANL  (input) LOGICAL
</span><span class="comment">*</span><span class="comment">          On entry, LTRANL specifies the op(TL):
</span><span class="comment">*</span><span class="comment">             = .FALSE., op(TL) = TL,
</span><span class="comment">*</span><span class="comment">             = .TRUE., op(TL) = TL'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LTRANR  (input) LOGICAL
</span><span class="comment">*</span><span class="comment">          On entry, LTRANR specifies the op(TR):
</span><span class="comment">*</span><span class="comment">            = .FALSE., op(TR) = TR,
</span><span class="comment">*</span><span class="comment">            = .TRUE., op(TR) = TR'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  ISGN    (input) INTEGER
</span><span class="comment">*</span><span class="comment">          On entry, ISGN specifies the sign of the equation
</span><span class="comment">*</span><span class="comment">          as described before. ISGN may only be 1 or -1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N1      (input) INTEGER
</span><span class="comment">*</span><span class="comment">          On entry, N1 specifies the order of matrix TL.
</span><span class="comment">*</span><span class="comment">          N1 may only be 0, 1 or 2.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N2      (input) INTEGER
</span><span class="comment">*</span><span class="comment">          On entry, N2 specifies the order of matrix TR.
</span><span class="comment">*</span><span class="comment">          N2 may only be 0, 1 or 2.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  TL      (input) REAL array, dimension (LDTL,2)
</span><span class="comment">*</span><span class="comment">          On entry, TL contains an N1 by N1 matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDTL    (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the matrix TL. LDTL &gt;= max(1,N1).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  TR      (input) REAL array, dimension (LDTR,2)
</span><span class="comment">*</span><span class="comment">          On entry, TR contains an N2 by N2 matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDTR    (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the matrix TR. LDTR &gt;= max(1,N2).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  B       (input) REAL array, dimension (LDB,2)
</span><span class="comment">*</span><span class="comment">          On entry, the N1 by N2 matrix B contains the right-hand
</span><span class="comment">*</span><span class="comment">          side of the equation.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDB     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the matrix B. LDB &gt;= max(1,N1).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  SCALE   (output) REAL
</span><span class="comment">*</span><span class="comment">          On exit, SCALE contains the scale factor. SCALE is chosen
</span><span class="comment">*</span><span class="comment">          less than or equal to 1 to prevent the solution overflowing.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  X       (output) REAL array, dimension (LDX,2)
</span><span class="comment">*</span><span class="comment">          On exit, X contains the N1 by N2 solution.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDX     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the matrix X. LDX &gt;= max(1,N1).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  XNORM   (output) REAL
</span><span class="comment">*</span><span class="comment">          On exit, XNORM is the infinity-norm of the solution.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          On exit, INFO is set to
</span><span class="comment">*</span><span class="comment">             0: successful exit.
</span><span class="comment">*</span><span class="comment">             1: TL and TR have too close eigenvalues, so TL or
</span><span class="comment">*</span><span class="comment">                TR is perturbed to get a nonsingular equation.
</span><span class="comment">*</span><span class="comment">          NOTE: In the interests of speed, this routine does not
</span><span class="comment">*</span><span class="comment">                check the inputs for errors.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      REAL               ZERO, ONE
      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
      REAL               TWO, HALF, EIGHT
      PARAMETER          ( TWO = 2.0E+0, HALF = 0.5E+0, EIGHT = 8.0E+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            BSWAP, XSWAP
      INTEGER            I, IP, IPIV, IPSV, J, JP, JPSV, K
      REAL               BET, EPS, GAM, L21, SGN, SMIN, SMLNUM, TAU1,
     $                   TEMP, U11, U12, U22, XMAX
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Arrays ..
</span>      LOGICAL            BSWPIV( 4 ), XSWPIV( 4 )
      INTEGER            JPIV( 4 ), LOCL21( 4 ), LOCU12( 4 ),
     $                   LOCU22( 4 )
      REAL               BTMP( 4 ), T16( 4, 4 ), TMP( 4 ), X2( 2 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      INTEGER            ISAMAX
      REAL               <a name="SLAMCH.115"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
      EXTERNAL           ISAMAX, <a name="SLAMCH.116"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           SCOPY, SSWAP
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          ABS, MAX
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Data statements ..
</span>      DATA               LOCU12 / 3, 4, 1, 2 / , LOCL21 / 2, 1, 4, 3 / ,
     $                   LOCU22 / 4, 3, 2, 1 /
      DATA               XSWPIV / .FALSE., .FALSE., .TRUE., .TRUE. /
      DATA               BSWPIV / .FALSE., .TRUE., .FALSE., .TRUE. /
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Do not check the input parameters for errors
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span>      IF( N1.EQ.0 .OR. N2.EQ.0 )
     $   RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Set constants to control overflow
</span><span class="comment">*</span><span class="comment">
</span>      EPS = <a name="SLAMCH.143"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'P'</span> )
      SMLNUM = <a name="SLAMCH.144"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'S'</span> ) / EPS
      SGN = ISGN
<span class="comment">*</span><span class="comment">
</span>      K = N1 + N1 + N2 - 2
      GO TO ( 10, 20, 30, 50 )K
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     1 by 1: TL11*X + SGN*X*TR11 = B11
</span><span class="comment">*</span><span class="comment">
</span>   10 CONTINUE
      TAU1 = TL( 1, 1 ) + SGN*TR( 1, 1 )
      BET = ABS( TAU1 )
      IF( BET.LE.SMLNUM ) THEN
         TAU1 = SMLNUM
         BET = SMLNUM
         INFO = 1
      END IF
<span class="comment">*</span><span class="comment">
</span>      SCALE = ONE
      GAM = ABS( B( 1, 1 ) )
      IF( SMLNUM*GAM.GT.BET )
     $   SCALE = ONE / GAM
<span class="comment">*</span><span class="comment">
</span>      X( 1, 1 ) = ( B( 1, 1 )*SCALE ) / TAU1
      XNORM = ABS( X( 1, 1 ) )
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     1 by 2:
</span><span class="comment">*</span><span class="comment">     TL11*[X11 X12] + ISGN*[X11 X12]*op[TR11 TR12]  = [B11 B12]
</span><span class="comment">*</span><span class="comment">                                       [TR21 TR22]
</span><span class="comment">*</span><span class="comment">
</span>   20 CONTINUE
<span class="comment">*</span><span class="comment">
</span>      SMIN = MAX( EPS*MAX( ABS( TL( 1, 1 ) ), ABS( TR( 1, 1 ) ),
     $       ABS( TR( 1, 2 ) ), ABS( TR( 2, 1 ) ), ABS( TR( 2, 2 ) ) ),
     $       SMLNUM )
      TMP( 1 ) = TL( 1, 1 ) + SGN*TR( 1, 1 )
      TMP( 4 ) = TL( 1, 1 ) + SGN*TR( 2, 2 )
      IF( LTRANR ) THEN
         TMP( 2 ) = SGN*TR( 2, 1 )
         TMP( 3 ) = SGN*TR( 1, 2 )
      ELSE
         TMP( 2 ) = SGN*TR( 1, 2 )
         TMP( 3 ) = SGN*TR( 2, 1 )
      END IF
      BTMP( 1 ) = B( 1, 1 )
      BTMP( 2 ) = B( 1, 2 )
      GO TO 40
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     2 by 1:
</span><span class="comment">*</span><span class="comment">          op[TL11 TL12]*[X11] + ISGN* [X11]*TR11  = [B11]
</span><span class="comment">*</span><span class="comment">            [TL21 TL22] [X21]         [X21]         [B21]
</span><span class="comment">*</span><span class="comment">
</span>   30 CONTINUE
      SMIN = MAX( EPS*MAX( ABS( TR( 1, 1 ) ), ABS( TL( 1, 1 ) ),
     $       ABS( TL( 1, 2 ) ), ABS( TL( 2, 1 ) ), ABS( TL( 2, 2 ) ) ),
     $       SMLNUM )
      TMP( 1 ) = TL( 1, 1 ) + SGN*TR( 1, 1 )
      TMP( 4 ) = TL( 2, 2 ) + SGN*TR( 1, 1 )
      IF( LTRANL ) THEN
         TMP( 2 ) = TL( 1, 2 )
         TMP( 3 ) = TL( 2, 1 )
      ELSE
         TMP( 2 ) = TL( 2, 1 )
         TMP( 3 ) = TL( 1, 2 )
      END IF
      BTMP( 1 ) = B( 1, 1 )
      BTMP( 2 ) = B( 2, 1 )
   40 CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Solve 2 by 2 system using complete pivoting.
</span><span class="comment">*</span><span class="comment">     Set pivots less than SMIN to SMIN.
</span><span class="comment">*</span><span class="comment">
</span>      IPIV = ISAMAX( 4, TMP, 1 )
      U11 = TMP( IPIV )
      IF( ABS( U11 ).LE.SMIN ) THEN
         INFO = 1
         U11 = SMIN
      END IF
      U12 = TMP( LOCU12( IPIV ) )
      L21 = TMP( LOCL21( IPIV ) ) / U11
      U22 = TMP( LOCU22( IPIV ) ) - U12*L21
      XSWAP = XSWPIV( IPIV )
      BSWAP = BSWPIV( IPIV )
      IF( ABS( U22 ).LE.SMIN ) THEN
         INFO = 1
         U22 = SMIN
      END IF
      IF( BSWAP ) THEN
         TEMP = BTMP( 2 )
         BTMP( 2 ) = BTMP( 1 ) - L21*TEMP
         BTMP( 1 ) = TEMP
      ELSE
         BTMP( 2 ) = BTMP( 2 ) - L21*BTMP( 1 )
      END IF
      SCALE = ONE
      IF( ( TWO*SMLNUM )*ABS( BTMP( 2 ) ).GT.ABS( U22 ) .OR.
     $    ( TWO*SMLNUM )*ABS( BTMP( 1 ) ).GT.ABS( U11 ) ) THEN
         SCALE = HALF / MAX( ABS( BTMP( 1 ) ), ABS( BTMP( 2 ) ) )
         BTMP( 1 ) = BTMP( 1 )*SCALE
         BTMP( 2 ) = BTMP( 2 )*SCALE
      END IF
      X2( 2 ) = BTMP( 2 ) / U22
      X2( 1 ) = BTMP( 1 ) / U11 - ( U12 / U11 )*X2( 2 )
      IF( XSWAP ) THEN
         TEMP = X2( 2 )
         X2( 2 ) = X2( 1 )
         X2( 1 ) = TEMP
      END IF
      X( 1, 1 ) = X2( 1 )
      IF( N1.EQ.1 ) THEN
         X( 1, 2 ) = X2( 2 )
         XNORM = ABS( X( 1, 1 ) ) + ABS( X( 1, 2 ) )
      ELSE
         X( 2, 1 ) = X2( 2 )
         XNORM = MAX( ABS( X( 1, 1 ) ), ABS( X( 2, 1 ) ) )
      END IF
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     2 by 2:
</span><span class="comment">*</span><span class="comment">     op[TL11 TL12]*[X11 X12] +ISGN* [X11 X12]*op[TR11 TR12] = [B11 B12]
</span><span class="comment">*</span><span class="comment">       [TL21 TL22] [X21 X22]        [X21 X22]   [TR21 TR22]   [B21 B22]
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Solve equivalent 4 by 4 system using complete pivoting.
</span><span class="comment">*</span><span class="comment">     Set pivots less than SMIN to SMIN.
</span><span class="comment">*</span><span class="comment">
</span>   50 CONTINUE
      SMIN = MAX( ABS( TR( 1, 1 ) ), ABS( TR( 1, 2 ) ),
     $       ABS( TR( 2, 1 ) ), ABS( TR( 2, 2 ) ) )
      SMIN = MAX( SMIN, ABS( TL( 1, 1 ) ), ABS( TL( 1, 2 ) ),
     $       ABS( TL( 2, 1 ) ), ABS( TL( 2, 2 ) ) )
      SMIN = MAX( EPS*SMIN, SMLNUM )
      BTMP( 1 ) = ZERO
      CALL SCOPY( 16, BTMP, 0, T16, 1 )
      T16( 1, 1 ) = TL( 1, 1 ) + SGN*TR( 1, 1 )
      T16( 2, 2 ) = TL( 2, 2 ) + SGN*TR( 1, 1 )
      T16( 3, 3 ) = TL( 1, 1 ) + SGN*TR( 2, 2 )
      T16( 4, 4 ) = TL( 2, 2 ) + SGN*TR( 2, 2 )
      IF( LTRANL ) THEN
         T16( 1, 2 ) = TL( 2, 1 )
         T16( 2, 1 ) = TL( 1, 2 )
         T16( 3, 4 ) = TL( 2, 1 )
         T16( 4, 3 ) = TL( 1, 2 )
      ELSE
         T16( 1, 2 ) = TL( 1, 2 )
         T16( 2, 1 ) = TL( 2, 1 )
         T16( 3, 4 ) = TL( 1, 2 )
         T16( 4, 3 ) = TL( 2, 1 )
      END IF
      IF( LTRANR ) THEN
         T16( 1, 3 ) = SGN*TR( 1, 2 )
         T16( 2, 4 ) = SGN*TR( 1, 2 )
         T16( 3, 1 ) = SGN*TR( 2, 1 )
         T16( 4, 2 ) = SGN*TR( 2, 1 )
      ELSE
         T16( 1, 3 ) = SGN*TR( 2, 1 )
         T16( 2, 4 ) = SGN*TR( 2, 1 )
         T16( 3, 1 ) = SGN*TR( 1, 2 )
         T16( 4, 2 ) = SGN*TR( 1, 2 )
      END IF
      BTMP( 1 ) = B( 1, 1 )
      BTMP( 2 ) = B( 2, 1 )
      BTMP( 3 ) = B( 1, 2 )
      BTMP( 4 ) = B( 2, 2 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Perform elimination
</span><span class="comment">*</span><span class="comment">
</span>      DO 100 I = 1, 3
         XMAX = ZERO
         DO 70 IP = I, 4
            DO 60 JP = I, 4
               IF( ABS( T16( IP, JP ) ).GE.XMAX ) THEN
                  XMAX = ABS( T16( IP, JP ) )
                  IPSV = IP
                  JPSV = JP
               END IF
   60       CONTINUE
   70    CONTINUE
         IF( IPSV.NE.I ) THEN
            CALL SSWAP( 4, T16( IPSV, 1 ), 4, T16( I, 1 ), 4 )
            TEMP = BTMP( I )
            BTMP( I ) = BTMP( IPSV )
            BTMP( IPSV ) = TEMP
         END IF
         IF( JPSV.NE.I )
     $      CALL SSWAP( 4, T16( 1, JPSV ), 1, T16( 1, I ), 1 )
         JPIV( I ) = JPSV
         IF( ABS( T16( I, I ) ).LT.SMIN ) THEN
            INFO = 1
            T16( I, I ) = SMIN
         END IF
         DO 90 J = I + 1, 4
            T16( J, I ) = T16( J, I ) / T16( I, I )
            BTMP( J ) = BTMP( J ) - T16( J, I )*BTMP( I )
            DO 80 K = I + 1, 4
               T16( J, K ) = T16( J, K ) - T16( J, I )*T16( I, K )
   80       CONTINUE
   90    CONTINUE
  100 CONTINUE
      IF( ABS( T16( 4, 4 ) ).LT.SMIN )
     $   T16( 4, 4 ) = SMIN
      SCALE = ONE
      IF( ( EIGHT*SMLNUM )*ABS( BTMP( 1 ) ).GT.ABS( T16( 1, 1 ) ) .OR.
     $    ( EIGHT*SMLNUM )*ABS( BTMP( 2 ) ).GT.ABS( T16( 2, 2 ) ) .OR.
     $    ( EIGHT*SMLNUM )*ABS( BTMP( 3 ) ).GT.ABS( T16( 3, 3 ) ) .OR.
     $    ( EIGHT*SMLNUM )*ABS( BTMP( 4 ) ).GT.ABS( T16( 4, 4 ) ) ) THEN
         SCALE = ( ONE / EIGHT ) / MAX( ABS( BTMP( 1 ) ),
     $           ABS( BTMP( 2 ) ), ABS( BTMP( 3 ) ), ABS( BTMP( 4 ) ) )
         BTMP( 1 ) = BTMP( 1 )*SCALE
         BTMP( 2 ) = BTMP( 2 )*SCALE
         BTMP( 3 ) = BTMP( 3 )*SCALE
         BTMP( 4 ) = BTMP( 4 )*SCALE
      END IF
      DO 120 I = 1, 4
         K = 5 - I
         TEMP = ONE / T16( K, K )
         TMP( K ) = BTMP( K )*TEMP
         DO 110 J = K + 1, 4
            TMP( K ) = TMP( K ) - ( TEMP*T16( K, J ) )*TMP( J )
  110    CONTINUE
  120 CONTINUE
      DO 130 I = 1, 3
         IF( JPIV( 4-I ).NE.4-I ) THEN
            TEMP = TMP( 4-I )
            TMP( 4-I ) = TMP( JPIV( 4-I ) )
            TMP( JPIV( 4-I ) ) = TEMP
         END IF
  130 CONTINUE
      X( 1, 1 ) = TMP( 1 )
      X( 2, 1 ) = TMP( 2 )
      X( 1, 2 ) = TMP( 3 )
      X( 2, 2 ) = TMP( 4 )
      XNORM = MAX( ABS( TMP( 1 ) )+ABS( TMP( 3 ) ),
     $        ABS( TMP( 2 ) )+ABS( TMP( 4 ) ) )
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="SLASY2.379"></a><a href="slasy2.f.html#SLASY2.1">SLASY2</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

</pre>

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